I agree with Kimball's answer. If I would like that somebody visits me but don't want to fund the visit, I would tell at the very beginning that I do not have funding for the visit. But then I would not call that an "invitation".
Sometimes people say something like "It would be great if you could visit our group when you are around." I would not call this an invitation but an "offer for deeper collaboration". If you've got some "invitation" like this and follow up on this by email, I would suggest to write something like "I would like visit and also could prepare a talk, but unfortunately, I do not have any funding available." (if this is true), and then see what reply you get.
If it is clear that the hosting group will not fund you, but you really want to go, then the first person to ask about funding is your advisor. More advice is not possible in general since universities/faculties/departments/groups differ a lot in this respect. Sometimes the department may have some travel money for which you may apply (but often this is not the case), sometimes there are other resources available, but a general advice is impossible.